Diffusion methods for classification with pairwise relationships

Abstract

We dene two algorithms for propagating information in classication problems with pairwise relationships. The algorithms involve contraction maps and are related to non-linear diusion and random walks on graphs. The approach is also related to message passing and mean eld methods. The algorithms we describe are guaranteed to converge on graphs with arbitrary topology. Moreover they always converge to a unique xed point, independent of initialization. We prove that the xed points of the algorithms under consideration dene lower-bounds on the energy function and the max-marginals of a Markov random eld. Our theoretical results also illustrate a relationship between message passing algorithms and value iteration for an innite horizon Markov decision process. We illustrate the practical feasibility of our algorithms with preliminary experiments in image restoration and stereo depth estimation.